| Author | Message | ||
     lee (leemu215) Member Username: leemu215 Post Number: 17 Registered: 06-2008 |
In the TENSION.PDE it is said that P = [Sx,Txy] and Q = [Txy,Sy] The "load" (or "natural") boundary condition for the U-equation defines the outward surface-normal component of P, while the load boundary condition for the V-equation defines the surface-normal component of Q. Thus, the load boundary conditions for the U- and V- equations together define the surface load vector. does it mean ,( n is the normal vector of surface)load(U)=P*n? is it OK to apply a boudary condition like Value(V)=something;Load(U)=someting? or Value(V)=something;Load(V)=someting? Thanks very much!! | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1177 Registered: 06-2003 |
1. If you define P=[Sx,Txy], then the x-component stress equation is Div(P)=0. FlexPDE integrates second order terms by parts, which generates surface integral terms. The Natural (Load) BC provides the integrands for these terms. Integration by parts is equivalent to the Divergence Theorem for this equation. The Divergence Theorem says Vol_Integral(Div(P)) = Surf_Integral(n<dot>P) with "n" the unit outward surface normal. The Natural BC for the x-component equation therefore supplies the values of n<dot>P. Similar arguments apply to the y-component equation. 2. You can apply one boundary condition for each variable on each boundary segment. "Value(V)=something; Load(U)=something" is therefore legal, while "Value(V)=something; Load(V)=something" is not. | ||
| lee (leemu215) Member Username: leemu215 Post Number: 18 Registered: 06-2008 |
thanks for your explanation.That helps a lot. |